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Simplifying 3a2 + -30a = 2 Reorder the terms: -30a + 3a2 = 2 Solving -30a + 3a2 = 2 Solving for variable 'a'. Reorder the terms: -2 + -30a + 3a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -30a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -10a + a2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -10a + 0.6666666667 + a2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -10a + a2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -10a + a2 = 0 + 0.6666666667 -10a + a2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -10a + a2 = 0.6666666667 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = 0.6666666667 + 25 Reorder the terms: 25 + -10a + a2 = 0.6666666667 + 25 Combine like terms: 0.6666666667 + 25 = 25.6666666667 25 + -10a + a2 = 25.6666666667 Factor a perfect square on the left side: (a + -5)(a + -5) = 25.6666666667 Calculate the square root of the right side: 5.066228051 Break this problem into two subproblems by setting (a + -5) equal to 5.066228051 and -5.066228051.Subproblem 1
a + -5 = 5.066228051 Simplifying a + -5 = 5.066228051 Reorder the terms: -5 + a = 5.066228051 Solving -5 + a = 5.066228051 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 5.066228051 + 5 Combine like terms: -5 + 5 = 0 0 + a = 5.066228051 + 5 a = 5.066228051 + 5 Combine like terms: 5.066228051 + 5 = 10.066228051 a = 10.066228051 Simplifying a = 10.066228051Subproblem 2
a + -5 = -5.066228051 Simplifying a + -5 = -5.066228051 Reorder the terms: -5 + a = -5.066228051 Solving -5 + a = -5.066228051 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -5.066228051 + 5 Combine like terms: -5 + 5 = 0 0 + a = -5.066228051 + 5 a = -5.066228051 + 5 Combine like terms: -5.066228051 + 5 = -0.066228051 a = -0.066228051 Simplifying a = -0.066228051Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.066228051, -0.066228051}
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